It is June 27th.
In 1844, “Joseph Smith the Prophet, and Hyrum Smith the Patriarch were shot in Carthage jail, on the 27th of June, 1844, about five o’clock p.m., by an armed mob — painted black — of from 150 to 200 persons.Hyrum was shot first and fell calmly, exclaiming: I am a dead man! Joseph leaped from the window, and was shot dead in the attempt, exclaiming: O Lord my God! They were both shot after they were dead, in a brutal manner, and both received four balls.” (John Taylor)
“John Taylor and Willard Richard, two of the Twelve, were the only persons in the room at the time; the former was wounded in a savage manner with four balls, but has since recovered; the latter, through the providence of God, escaped, without even a hole in his robe. Hyrum Smith was forty-four years old in February 1844 and Joseph Smith was thirty-eight in December, 1843.” (Doctrine & Covenants 135)
More images of the Carthage Jail
History of The Church, vol 6
featured photo: Gary E. Smith